5 research outputs found
The k-Server with Preferences Problem
The famous -Server Problem covers plenty of resource allocation scenarios,
and several variations have been studied extensively. However, to the best of
our knowledge, no research has considered the problem if the servers are not
identical and requests can express which servers should serve them. Therefore,
we present a new model generalizing the -Server Problem by preferences of
the requests and study it in uniform metrics for deterministic online
algorithms. In our model, requests can either demand to be answered by any
server (general requests) or by a specific one (specific requests). If only
general requests appear, the instance is one of the -Server Problem, and a
lower bound for the competitive ratio of applies. If only specific requests
appear, a competitive ratio of becomes trivial since there is no freedom
regarding the servers' movements. We show that if both kinds of requests
appear, the lower bound raises to . We study deterministic online
algorithms in uniform metrics and present two algorithms. The first one has a
competitive ratio dependent on the frequency of specific requests. It achieves
a worst-case competitive ratio of while it is optimal when only general
or only specific requests appear (ratio of and ). The second has a
close-to-optimal worst-case competitive ratio of . For the first
algorithm, we show a lower bound of , while the second one has one of
when only general requests appear. Both algorithms differ in only one
behavioral rule for each server that significantly influences the competitive
ratio. Each server acting according to the rule allows approaching the
worst-case lower bound, while it implies an increased lower bound for
-Server instances. Thus, there is a trade-off between performing well
against instances of the -Server Problem and ones containing specific
requests.Comment: A conference version of this paper was accepted at the 34th ACM
Symposium on Parallelism in Algorithms and Architectures (SPAA 2022